Raman spectra of cubic and amorphous Ge${}_2$Sb${}_2$Te${}_5$ from first principles

We computed the Raman spectrum of cubic and amorphous Ge${}_2$Sb${}_2$Te${}_5$ (GST) by ab initio phonons and an empirical bond polarizability model. Models of the amorphous phase were generated by quenching from the melt by means of ab initio molecular dynamics simulations. The calculated spectra are in good agreement with experimental data which confirms the reliability of the models of the amorphous phase emerged from the simulations. All the features of the spectrum in both crystalline and amorphous GST can be assigned to vibrations of defective octahedra. The calculations reveal that the polarizability of the Sb-Te is much higher than that of Ge-Te bonds and of Ge-Ge/Sb wrong bonds resulting in a much lower Raman response of tetrahedra which are made of Ge-Te and wrong bonds. As a consequence and as opposed to amorphous GeTe, the signatures of tetrahedra in the Raman spectrum of amorphous GST are hidden by the larger Raman cross section of defective octahedra.

Figure 1

Raman spectrum of crystalline Sb${}_2$Te${}_3$ computed within the BPM (continuous line) and ab initio from Ref. 25 (dashed line).

Figure 2

Raman spectrum of hexagonal GST computed within the BPM (continuous line) and ab initio from Ref. 26 (dashed line). We considered the two different stackings of the Ge-Sb planes named stacking A and B in Ref. 26 which correspond to the structures proposed in Ref. 27 and Ref. 28, respectively.

Figure 3

Raman spectrum of a small cell of GeSb${}_2$Te${}_4$ within the BPM (continuous line) and ab initio (dashed line).

Figure 4

Distribution of bond lengths for (a) Ge in tetrahedral (tetra) and defective octahedral sites and for (b) Sb with different coordination in a-GST. Inset: Sketch of the most frequent local geometries in a-GST corresponding to defective octahedral sites of 4-coordinated Ge and Sb and 3-coordinated Te.[10, 11]

Figure 5

Distribution of the three shorter (continuous line) and the other, longer (dashed) bond lengths for (a) Ge and (b) Sb in defective octahedral sites with different coordination in a-GST.

Figure 6

Upper panel: Distribution of bond lengths for (a) Ge and (b) Sb in cubic GST. Lower panel: Distribution of the three shorter (continuous line) and the other, longer (dashed) bond lengths for (a) Ge and (b) Sb in cubic GST.

Figure 7

Reduced Raman spectrum of (a) a-GST and (b) crystalline c-GST, computed within the BPM (continuous line) for unpolarized light in backscattering geometry compared with the analogous experimental spectra (dashed line) from Ref. 5. The reduced spectrum is obtained by multiplying by ${\omega }_S^{-4}\omega {}^1(n_B+1){}^{-1}$ the Raman scattering (Stokes) cross section given in Eq. (1). The theoretical spectra are obtained by substituting the $\delta$ functions in Eq. (1) with Lorentzian functions 5 cm${}^{-1}$ wide. We averaged over all possible incident directions of the light as in Eq. (5).

Figure 8

Raman spectra in HV and VV scattering geometries for (a) a-GST and (b) c-GST computed within the BPM (continuous line) and measured experimentally (dashed line, only for as-deposited a-GST) in Ref. 8.

Figure 9

Comparison of the experimental (Ref. 5) and theoretical reduced Raman spectra for two different models of a-GST, 270 atoms and 297 atoms large.

Figure 10

Projection of the reduced Raman spectrum in Fig. 7 on different types of atoms for (a) a-GST and (b) c-GST. Gt indicates tetrahedral germanium and Ge octahedral-like germanium.

Figure 11

Projection of the reduced Raman spectra in Fig. 7 on different types of bonds for (a) a-GST and (b) c-GST. Gt indicates tetrahedral germanium and Ge octahedral-like germanium.

Figure 12

Reduced Raman spectrum of a-GST in Fig. 7 (continuous line) compared with the spectrum computed by setting the BPM parameters of the Sb-Te bonds equal to those of the Ge-Te bond (cf. Table ) (dashed line).

Figure 13

Theoretical reduced Raman spectrum of a-GST and a-Sb${}_2$Te${}_3$ (see text) computed with the BPM model for unpolarized light in backscattering geometry. The calculation details are the same as those provided in the caption of Fig. 7.

Figure 14

Total projections of the reduced Raman spectrum on bending- and stretching-like displacements of atoms in pyramidal units. The projections were obtained by summing up the contributions of all the structural units. Total refers to the original Raman spectrum. The sum of the projections is not normalized to the total spectrum because of double counting (e.g., a Te atom belongs to a few GeTe${}_3$ units). The projection on stretching-like modes is defined as the projection on displacements of each Ge/Sb and Te along the direction defined by the height of the Te(Ge/Sb)${}_3$ and (Ge/Sb)Te${}_{3-n}$(Ge/Sb)${}_n$ pyramids [e.g., the direction ${\sum }_i\mathbf{x}(\mathrm{Te})-\mathbf{x}((\mathrm{Ge}/\mathrm{Sb}){}_i)$ for the Te(Ge/Sb)${}_3$ unit]. The projection on bending-like modes is defined as the projection of displacements of each Ge/Sb and Te atom on the two directions perpendicular to the stretching direction defined above.